In known prior art systems, the controller for the means for displacing the tool carriage is controlled by a memory in which the displacements of the tool carriage associated with each increment of angular movement of the crankshaft are stored, and the movement imparted to the tool by the tool carriage in dependence on the reference inputs and on the rotation of the workpiece result in combination in a machining of the contoured surface. Known control systems of that kind have the disadvantage that the data for the displacement of the tool carriage in dependence on the angular movement of the crankshaft, which data depend on data relating to the workpiece, must be computed and stored. A decisive other disadvantage resides in that any variations of the actual angular movement of the crankshaft will directly influence the drive means for the tool carriage because the angular position data are derived from the rotating crankshaft by a pulse generator. As a result, the inevitable vibrations and rotational oscillations of the crankshaft being milled influence the translational movement of the tool carriage and may even be amplified as they are transmitted. Owing to this virtually rigid coupling between the drive means for rotating the crankshaft and the drive means for displacing the tool carriage, the tolerance with which the crankshafts can be machined cannot be decreased as much as would be desired. This causes a significant barrier to the degree of precision which may be obtained in crankshaft milling using those approaches.